I've never asked Mr Cessna why side slipping with full flaps on the 172s I've flown is prohibited, but it certainly is not allowed in the POH.
There is a view amongst some jocks with much more experience than me that the 172 can stall with a very big wing drop and enter into a spin when slipping with full flaps if the airspeed is allowed to decay , but as I say, I've always followed the rules.
Having slipped PA28s extensively, its a great way to lose height rapidly and anyone who hasn't learned it would do well to spend some time with an instructor - the best thing is as soon as you remove the cross controls, the aircraft flies completely normally again, not pitch up or down as experienced when latering the flap settings in some aircraft.